# packages
library(tidyverse)
library(googlesheets4)
library(here)
library(metafor)
library(metaAidR)  # see a note above
library(orchaRd)  # see a note above
library(ape)
library(clubSandwich)
library(metaAidR)
library(patchwork)
library(emmeans)  # see a note above
library(kableExtra)
library(GGally)
library(cowplot)
library(grDevices)  # reqired for using base and ggplots together

# Below is the custom function to calculate the lnRR
lnRR_func <- function(Mc, Nc, Me, Ne, aCV2c, aCV2e, rho = 0.5) {
    lnRR <- log(Me/Mc) + 0.5 * ((aCV2e/Ne) - (aCV2c/Nc))

    var_lnRR <- (aCV2c/Nc) + (aCV2e/Ne) - 2 * rho * ((aCV2c * aCV2e)/sqrt(Nc * Ne))

    data.frame(lnRR, var_lnRR)
}

# Mc: Concentration of PFAS of the raw (control) sample Nc: Sample size of the
# raw (control) sample Me: Concentration of PFAS of the cooked (experimental)
# sample Ne: Sample size of the cooked (experimental) sample aCV2c: Mean
# coefficient of variation of the raw (control) samples aCV2e: Mean coefficient
# of variation of the cooked (experimental) samples